Editing Prime modulus multiplicative linear congruential generator

The '''prime modulus multiplicative linear congruential generator''' is a special type of 
[[linear congruential generator]], given by:
:<math>y_{n+1}\equiv ay_n + b  \qquad({\mathrm {mod}} ~m),</math>

The parameter <math>m</math>
should be prime and as large as possible without causing a numerical overflow
on the computer that it is running on.
For example, for a 32-bit (31 bit + 1 sign bit) word size
then the logical choice of <math>m</math> is the Mersenne prime

:<math>\left.m\right.=2^{31} -1=2147483647</math>,

with  <math>a=7^5</math> (a positive primitive root of <math>m</math> see Ref.s 1 and 2),
and <math>b=0</math>.
With these parameters one is able to generate a series of
<math>2.147 \times 10^9</math>
pseudo-random numbers from one seed value.
For an interesting  discussion on how  to choose an initial seed value see Ref. 3.
For a list of other values of <math>m</math> and <math>a</math> see Ref.4
and for its use on 64-bit computers see Ref. 5.

==References==
#[http://dx.doi.org/10.1145/365696.365712 D. W. Hutchinson, "A New Uniform Pesudorandom Number Generator", Communications of the ACM, '''9''' pp. 432-433 (1966)]
#[http://www.research.ibm.com/journal/sj/082/ibmsj0802D.pdf P. A. W.  Lewis and A. S. Goodman and J. M. Miller, "A pseudo-random number generator for the System/360", IBM Systems Journal  '''2''' pp. 136 (1969)]
#[http://dx.doi.org/10.1145/769800.769827 G. Marsaglia, "Seeds for Random Number Generators",Communications of the ACM, '''46''' pp. 90-93 (2003)]
#[http://dx.doi.org/10.1090/S0025-5718-99-00996-5 Pierre L'Ecuyer, "Tables of linear congruential generators of different sizes and good lattice structure", Mathematics of Computation, '''68''' pp. 249 - 260  (1999)]
#[http://dx.doi.org/10.1016/S0010-4655(97)00052-0   Iosif G. Dyadkin and Kenneth G. Hamilton "A study of 64-bit multipliers for Lehmer pseudorandom number generators", Computer Physics Communications  pp. 103-130 (1997)]

[[Category: Random numbers]]